In this paper, we present a method for segmenting phase contrast volume images of fibrous materials into fibre and background. The method is based on graph cut segmentation, and s tested on high resolution X-ray microtomography volume images of wood fibres in paper an composites. The new method produces better results than a standard method based on edge-preserving smoothing and hysteresis thresholding. The most important improvement is that the proposed method handles thick and collapsed fibres more accurately than previous methods.